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A Markovian queue with a single server having customer with impatient and server in different phases is examined. The server will be staying at sleep or active mode randomly and alternatively. The active mode comprises of two phases, the full active mode (FA) and slow active mode (SA). When the server is in full active mode, customers arrive and get service in FCFS queue discipline. However, when the server changes from full active to slow active, it will be able to service only in a lower rate lesser than that of full active mode. When the server is in slow active, none of the customer will be accepted to access the system and each of the customers will activate the impatient timer independently and quits the system if they are not served before the timer ends. In active or slow mode, the server may immediately switch to sleep mode (SL) when the very last available customer in the queue is served. The customers are not able to accept to admit the queue when the server is in SL and SA. After the sleep mode, the server will immediately switch to the fully active mode. We have acquired few metrics for the performance as well formulations for the time-independent state probabilities. Finally, extensive results are presented graphically to highlight the vitality of the system characteristics pertaining to the vital performance matrices.

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Evaluation of Multiple Phases of the Server in the Simple Queue, Subject to Customer Impatience

  • 会议论文

  • 发表日期：

    2025年

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  • C. T. Dora Pravina,
  • P. Kamala,
  • S. Sreelakshmi,
  • D. Kanagajothi,
  • R. Shanmugapriya

摘要

A Markovian queue with a single server having customer with impatient and server in different phases is examined. The server will be staying at sleep or active mode randomly and alternatively. The active mode comprises of two phases, the full active mode (FA) and slow active mode (SA). When the server is in full active mode, customers arrive and get service in FCFS queue discipline. However, when the server changes from full active to slow active, it will be able to service only in a lower rate lesser than that of full active mode. When the server is in slow active, none of the customer will be accepted to access the system and each of the customers will activate the impatient timer independently and quits the system if they are not served before the timer ends. In active or slow mode, the server may immediately switch to sleep mode (SL) when the very last available customer in the queue is served. The customers are not able to accept to admit the queue when the server is in SL and SA. After the sleep mode, the server will immediately switch to the fully active mode. We have acquired few metrics for the performance as well formulations for the time-independent state probabilities. Finally, extensive results are presented graphically to highlight the vitality of the system characteristics pertaining to the vital performance matrices.